Subgroups — #28476339

Order 15104.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21426371	C₂	1	1	yes	maximal, characteristic
2	#21422168	C₂	1	1	yes	maximal, characteristic
3	C₅₉×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	#16837807	—	2	1	no	—
5	#16837228	—	2	1	no	—
6	#16837228	C₄	1	2	yes	—
7	#16837155	—	2	1	no	—
8	C₂×C₃₂×C₅₉	—	2	1	no	—
9	C₄×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
10	#14273727	—	4	1	no	—
11	#14273661	—	2	2	no	—
12	#14273661	—	4	1	no	—
13	C₄⋊(C₅₉⋊C₈)	—	4	1	no	—
14	C₂×C₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₅₉	D₄	1	1	yes	characteristic
16	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
17	C₃₂×C₅₉	—	4	1	no	—
18	C₂×Dic₁₁₈	—	8	1	no	—
19	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₈×C₅₉	SD₁₆	1	1	yes	characteristic
21	C₄²×C₅₉	D₈	1	1	yes	characteristic
22	C₄⋊Dic₅₉	—	4	2	no	—
23	C₄⋊Dic₅₉	—	8	1	no	—
24	C₂×C₅₉⋊C₈	—	8	1	no	—
25	C₁₆×C₅₉	—	2	1	no	—
26	C₁₆×C₅₉	SD₁₆	1	1	yes	characteristic
27	C₁₆×C₅₉	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₅₉	#102	1	1	yes	characteristic
29	C₂×C₄×C₅₉	D₁₆	1	1	yes	characteristic
30	C₂×C₄×C₅₉	SD₃₂	1	1	yes	characteristic
31	C₂×Dic₅₉	—	8	2	no	—
32	Dic₁₁₈	—	16	1	no	—
33	Dic₁₁₈	—	16	1	no	—
34	C₈×C₅₉	—	2	1	no	—
35	C₈×C₅₉	#101	1	1	yes	characteristic
36	C₈×C₅₉	#103	1	1	yes	characteristic
37	C₅₉⋊C₈	—	16	1	no	—
38	#7450	—	59	1	no	maximal, Sylow
39	C₂²×C₅₉	#357	1	1	yes	characteristic
40	C₄×C₅₉	—	2	1	no	—
41	C₄×C₅₉	#332	1	1	yes	characteristic
42	C₄×C₅₉	#362	1	1	yes	characteristic
43	C₄×C₅₉	D₃₂	1	1	yes	characteristic
44	C₄×C₅₉	SD₆₄	1	1	yes	characteristic
45	Dic₅₉	—	16	2	no	—
46	#2252	—	59	1	no	—
47	C₄⋊C₃₂	D₅₉	1	1	yes	characteristic
48	#1371	—	59	1	no	—
49	C₂×C₅₉	#1364	1	1	yes	characteristic
50	C₂×C₅₉	#1415	1	1	yes	characteristic
51	C₂×C₅₉	#1420	1	1	yes	characteristic
52	#500	—	118	1	no	—
53	C₂×C₃₂	—	2	1	no	—
54	#366	—	59	2	no	—
55	#366	—	118	1	no	—
56	C₄×C₁₆	C₂×D₅₉	1	1	yes	characteristic
57	#335	—	118	1	no	—
58	C₅₉	#7450	1	1	yes	characteristic, complemented, Sylow
59	C₄⋊Q₈	—	236	1	no	—
60	C₂×C₁₆	C₄×D₅₉	1	1	yes	characteristic
61	C₂×C₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
62	#107	—	118	2	no	—
63	#107	—	236	1	no	—
64	C₄⋊C₈	—	236	1	no	—
65	C₄×C₈	D₂₃₆	1	1	yes	characteristic
66	C₃₂	—	4	1	no	—
67	C₂×Q₈	—	472	1	no	—
68	C₂×C₈	—	472	1	no	—
69	C₂×C₈	#11745660	1	1	yes	characteristic
70	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
71	C₄⋊C₄	—	472	1	no	—
72	C₄⋊C₄	—	236	2	no	—
73	C₄²	D₄₇₂	1	1	yes	characteristic
74	C₁₆	—	2	1	no	—
75	C₁₆	#11745670	1	1	yes	characteristic
76	C₁₆	#11745672	1	1	yes	characteristic
77	Q₈	—	944	1	no	—
78	Q₈	—	944	1	no	—
79	C₂×C₄	—	472	2	no	—
80	C₂×C₄	#14273649	1	1	yes	characteristic
81	C₂×C₄	D₉₄₄	1	1	yes	characteristic
82	C₂×C₄	#14273672	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	944	1	no	—
85	C₈	#14273645	1	1	yes	characteristic
86	C₈	#14273650	1	1	yes	characteristic
87	C₂²	#16837204	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	944	2	no	—
90	C₄	#16837147	1	1	yes	characteristic
91	C₄	#16837219	1	1	yes	characteristic
92	C₄	D₁₈₈₈	1	1	yes	characteristic
93	C₄	#16837241	1	1	yes	characteristic
94	C₂	#21422150	1	1	yes	characteristic
95	C₂	#21422275	1	1	yes	characteristic
96	C₂	#21422290	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16837204
commutator	C₂×C₁₆×C₅₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₅₉
Fitting	C₅₉×C₄⋊C₃₂	C₂
socle, prime radical	C₂²×C₅₉	#357
cosocle	C₄×C₁₆×C₅₉	C₂²
hypercenter	C₄⋊C₃₂	D₅₉
hypocenter	C₅₉	#7450
LCS	G ▷ C₂×C₁₆×C₅₉ ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄⋊C₃₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
58. C₅₉	#7450	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#21426371	2
#21422168	2
C₅₉×C₄⋊C₃₂	2
#7450	59